Related papers: Region growing for multi-route cuts
In the vertex connectivity survivable network design problem we are given an undirected graph G = (V,E) and connectivity requirement r(u,v) for each pair of vertices u,v. We are also given a cost function on the set of edges. Our goal is to…
The 2-Edge-Connected Spanning Subgraph problem (2ECSS) is among the most basic survivable network design problems: given an undirected and unweighted graph, the task is to find a spanning subgraph with the minimum number of edges that is…
In spatially embedded networks such as transportation and power grids, understanding how edge removals affect connectivity is crucial for robustness analysis. This paper studies a planar graph dismantling problem under an edge-budget…
There are many applications of graph cuts in computer vision, e.g. segmentation. We present a novel method to reformulate the NP-hard, k-way graph partitioning problem as an approximate minimal s-t graph cut problem, for which a globally…
Li and Panigrahi, in recent work, obtained the first deterministic algorithm for the global minimum cut of a weighted undirected graph that runs in time $o(mn)$. They introduced an elegant and powerful technique to find isolating cuts for a…
Consider the following "local" cut-detection problem in a directed graph: We are given a seed vertex $x$ and need to remove at most $k$ edges so that at most $\nu$ edges can be reached from $x$ (a "local" cut) or output $\bot$ to indicate…
Karger (SIAM Journal on Computing, 1999) developed the first fully-polynomial approximation scheme to estimate the probability that a graph $G$ becomes disconnected, given that its edges are removed independently with probability $p$. This…
We give an $n^{2+o(1)}$-time algorithm for finding $s$-$t$ min-cuts for all pairs of vertices $s$ and $t$ in a simple, undirected graph on $n$ vertices. We do so by constructing a Gomory-Hu tree (or cut equivalent tree) in the same running…
We study multi-budgeted variants of the classic minimum cut problem and graph separation problems that turned out to be important in parameterized complexity: Skew Multicut and Directed Feedback Arc Set. In our generalization, we assign…
For a connected graph, a {\em minimum vertex separator} is a minimum set of vertices whose removal creates at least two connected components. The vertex connectivity of the graph refers to the size of the minimum vertex separator and a…
We study the problem of maximizing the number of spanning trees in a connected graph by adding at most $k$ edges from a given candidate edge set. We give both algorithmic and hardness results for this problem: - We give a greedy algorithm…
We study graph partitioning problems from a min-max perspective, in which an input graph on n vertices should be partitioned into k parts, and the objective is to minimize the maximum number of edges leaving a single part. The two main…
Let $G=(V,E)$ be a multigraph (it has multiple edges, but no loops). The edge connectivity, denoted by $\lambda(G)$, is the cardinality of a minimum edge-cut of $G$. We call $G$ maximally edge-connected if $\lambda(G)=\delta(G)$, and $G$…
We prove essentially tight lower bounds, conditionally to the Exponential Time Hypothesis, for two fundamental but seemingly very different cutting problems on surface-embedded graphs: the Shortest Cut Graph problem and the Multiway Cut…
We develop a novel distributed algorithm for the minimum cut problem. We primarily aim at solving large sparse problems. Assuming vertices of the graph are partitioned into several regions, the algorithm performs path augmentations inside…
We study a large family of graph covering problems, whose definitions rely on distances, for graphs of bounded cyclomatic number (that is, the minimum number of edges that need to be removed from the graph to destroy all cycles). These…
Emerging reconfigurable optical communication technologies allow to enhance datacenter topologies with demand-aware links optimized towards traffic patterns. This paper studies the algorithmic problem of jointly optimizing topology and…
We study the classic Max-Cut problem under multiple cardinality constraints, which we refer to as the Constrained Max-Cut problem. Given a graph $G=(V, E)$, a partition of the vertices into $c$ disjoint parts $V_1, \ldots, V_c$, and…
We consider the following "multiway cut packing" problem in undirected graphs: we are given a graph G=(V,E) and k commodities, each corresponding to a set of terminals located at different vertices in the graph; our goal is to produce a…
Several important tasks in medical image analysis can be stated in the form of an optimization problem whose feasible solutions are connected subgraphs. Examples include the reconstruction of neural or vascular structures under…